Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

Combining selection valve and mixing chamber for nanoflow gradient generation: Toward developing a liquid chromatography cartridge coupled with mass spectrometer for protein and peptide analysis

Toward developing a micro HPLC cartridge, we have recently built a high-pressure electroosmotic pump (EOP). However, we do not recommend people to use this pump to deliver an organic solvent directly, because it often makes the pump rate unstable. We have experimented several approaches to address this issue, but none of them are satisfactory. Here, we develop an innovative approach to address this issue. We first create an abruption (a dead-volume) within a fluid conduit. We then utilize an EOP to withdraw, via a selection valve, a train of eluent solutions having decreasing eluting power into the fluid conduit. When these solutions are further aspirated through the dead-volume, these solutions are partially mixed, smoothening concentration transitions between two adjacent eluent solutions. As these solutions are pushed back, through the dead-volume again, a smooth gradient profile is formed. In this work, we characterize this scheme for gradient formation, and we incorporate this approach with a high-pressure EOP, a nanoliter injection valve, and a capillary column, yielding a micro HPLC system. We then couple this micro HPLC with an electrospray ionization – mass spectrometer for peptide and protein separations and identifications.     

Local-in-time adjoint-based method for design optimization of unsteady flows

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.     

Determination of Cr(VI) by portable tungsten coil electrothermal atomic absorption spectrometer after surfactant-assisted dispersive liquid-liquid microextraction

As a new developed instrument, a portable tungsten coil electrothermal atomic absorption spectrometer (W-coil ET-AAS) was first coupled with surfactant assisted dispersive liquid–liquid microextraction (SA-DLLME) to improve its analytical performance and expand its applications in this work. SA-DLLME was very simple, rapid and the extraction efficiency was considerably improved by the effect of surfactant, which was suitable to be coupled with the portable instrument in field analysis. After SA-DLLME, concentrated chromium in organic phase was directly determined on W-coil atomiser. The influence factors relevant to SA-DLLME and instrumental conditions were studied systematically. Under the optimal conditions, the limit of detection (LOD) for Cr(VI) was 0.016 µg L^?1, with sensitivity enhancement factor (EF) of 107. The relative standard deviation (RSD) for seven replicate measurements of 0.5 µg L^?1 of Cr(VI) was 4.6%. The recoveries for the spiked samples were in the acceptable range of 96.8–104%. The rapid, simple and high effective method greatly improved the sensitivity of this portable spectrometer for the determination of Cr(VI) and was applied to the analysis of ultra-trace Cr(VI) in real and certified water samples with satisfactory results.     

Detection of NMR signals with a radio-frequency atomic magnetometer

We demonstrate detection of proton NMR signals with a radio-frequency (rf) atomic magnetometer tuned to the NMR frequency of 62 kHz. High-frequency operation of the atomic magnetometer makes it relatively insensitive to ambient magnetic field noise. We obtain magnetic field sensitivity of 7 fT/Hz1/2 using only a thin aluminum shield. We also derive an expression for the fundamental sensitivity limit of a surface inductive pick-up coil as a function of frequency and find that an atomic rf magnetometer is intrinsically more sensitive than a coil of comparable size for frequencies below about 50 MHz.     

An optimization method for designing SENSE imaging RF coil arrays

An optimization method in RF coil array design for SENSE imaging is described. Using this method the optimized RF coil geometries can be calculated numerically given the required SENSE imaging performance. Although this method can be applied to optimize the RF coil arrays for both 1D and 2D SENSE imaging, to demonstrate the potential applications of this method, we designed RF coil arrays for 2D SENSE imaging and compared their performance by simulation. An optimized 4-channel receive-only RF coil array designed for 2D SENSE imaging was implemented and tested to demonstrate the feasibility of the proposed technique. Imaging results showed reasonable agreement with the simulations, thus the method can be applied to RF coil array designs for SENSE imaging when optimum imaging performance is desired.     

4T split TEM volume head and knee coils for improved sensitivity and patient accessibility

Split RF coils offer improved patient access by eliminating the need for the coil to be slid over the region of interest. For unshielded birdcage coils, the presence of end ring currents necessitates a direct electrical connection between two halves of the coil. For high-field (>3T) shielded birdcage coils, both the shield and the coil must be split and reliably connected electrically. This problem can be circumvented by the use of split TEM volume coils. Since the elements of a TEM coil are coupled inductively, no direct electrical connection between the halves is necessary. In this work we demonstrate that the effects of splitting the shield for head and knee TEMs can be compensated for, and performance retained. For the knee, the improved access allowed the coil diameter to be reduced, enhancing the sensitivity by 15-20%.